Constants of a Child Universe

The Constants of a Child Universe are the rule by which a universe's Tempo and Length set all its constants: its frame ratio s′ = ①⥂⧗′⌂/ℨ, its quantum of action ℏ′ = s′² · ℏ_ℨ, its light speed 𝒞→′ = ①⥂⦜′⌂/①⥂⧗′⌂, its Planck mass and its G, with Boltzmann's constant the one constant every universe shares. Three Planck values fix three constants. A child's Tempo comes from its Null Well's mass, ①⥂⧗′⌂ = ①⥂⧗⌂ · (M_null/M_P)^½, and its Length from its parent's singularity, ①⥂⦜′⌂ = 2 · ①⊕′⌂. The third comes from the Zinf reduction: a local pulse lasts s′ Zinf cycles and carries s′ Zinf units of energy, so its action is s′² Zinf actions, with ℏ_ℨ = ℏ/s² ≈ 1.892 × 10⁻¹⁵⁹ J·s, which returns our ℏ at s ≈ 2.361 × 10⁶². On the typical ladder, where Tempo and Diameter both grow by 2f a level, the rule returns the Zinf reduction exactly: mass falls by s, 𝒞→ and G come out unchanged, and ℏ grows as s². Off the ladder 𝒞→′ shifts and G′ shifts as its fifth power, so light speed is a birth property of a universe, fixed within it and different between universes. Only k_B carries through, because a bit is one bit of entropy, k_B ln 2, in every universe: information constants carry through, geometric constants are born. In the parameters of Chapter 6, α = ①⥂⧗′⌂/①⥂⧗⌂, β = λ/α with λ the ratio of Lengths, δ = α² and γ = β⁵, which meets α²·β⁵ = γ·δ identically. Whether the fine-structure constant differs between universes depends on how charge scales, which the theory leaves open. Formally, s′ = ①⥂⧗′⌂/ℨ [∅], ℏ′ = s′² · ℏ_ℨ [𝕄·𝕃²·𝕋⁻¹], 𝒞→′ = ①⥂⦜′⌂/①⥂⧗′⌂ [𝕃·𝕋⁻¹], m′ = ℏ′ · ①⥂⧗′⌂/①⥂⦜′⌂² [𝕄], G′ = ①⥂⦜′⌂³/(m′ · ①⥂⧗′⌂²) [𝕄⁻¹·𝕃³·𝕋⁻²] and k_B′ = k_B [𝕄·𝕃²·𝕋⁻²·Θ⁻¹]. It connects to Bits per Pulse, The Universal Scaling Factor, Base Units at Substrate ℨinf Scale, Pulse Diameter Variability, Local Pulse Tempo / Planck Time Relation, Dimensional Consistency Constraint and Planck Mass.

Category: Manuscript

Chapter: Chapter 1

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